Birational equivalences and Kac-Moody algebras

We show that every Kac-Moody algebra is birationally equivalent to a smash biproduct of two copies of a Weyl algebra together with a polynomial algebra. We also show that the same is true for quantized Kac-Moody algebras where one replaces Weyl algebras with their quantum analogues.

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Bibliographische Detailangaben
Veröffentlicht in:	Bulletin des sciences mathématiques 2024-07, Vol.193, p.103451, Article 103451
1. Verfasser:	Kaygun, Atabey
Format:	Artikel
Sprache:	eng
Schlagworte:	Birational equivalence Gelfand-Kirillov conjecture Kac-Moody algebras Quantized Kac-Moody algebras
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Beschreibung
Zusammenfassung:	We show that every Kac-Moody algebra is birationally equivalent to a smash biproduct of two copies of a Weyl algebra together with a polynomial algebra. We also show that the same is true for quantized Kac-Moody algebras where one replaces Weyl algebras with their quantum analogues.
ISSN:	0007-4497 1952-4773
DOI:	10.1016/j.bulsci.2024.103451